# The pressure acting on 500 cubic meters of gas is reduced from 4 atm to 2 atm. If the temperature remains constant, what is the new volume?

Mar 2, 2016

${\text{V"_"new"="1000 m}}^{3}$

#### Explanation:

We will use Boyle's law, which states that pressure and volume are inversely proportional at constant temperature. We can express this mathematically as:

${\text{P"_1"V"_1="P"_2"V}}_{2}$

Here, we see that

$\text{P"_1="4 atm}$
$\text{P"_2="2 atm}$

${\text{V"_1="500 m}}^{3}$
$\text{V"_2="unknown}$

We want to manipulate Boyle's law to solve for ${\text{V}}_{2}$:

"V"_2=("P"_1"V"_1)/("P"_2)

Plugging in what we know:

"V"_2=("4 atm" * "500 m"^3)/("2 atm")

${\text{V"_2=2 * "500 m}}^{3}$

${\text{V"_2="1000 m}}^{3}$

We can see that the volume increased from ${\text{500 m}}^{3}$ to ${\text{1000 m}}^{3}$, so it doubled. This is paired with the pressure being halved, as should be the case in an inversely proportional relationship.